Lecture

# LCN2 Seminar: Estimating tails of degree distributions in complex networks, a tale of extremes

- Pim van der Hoorn (TUe)

- Date
- Friday 29 October 2021
- Time
- Location
- Gorlaeus building
- Room
- Science club

## Or attend via Zoom

Zoom link## 48th LCN2 seminar

**Speaker:** Pim van der Hoorn (TUe)

**Title**: Estimating tails of degree distributions in complex networks, a tale of extremes

**Abstract: **

'A common first-order property of networks that is often studied is the distribution of the degrees of its nodes. When researchers started looking at these distributions, they made an interesting discovery. For many networks, coming from a variety of different domains, the degree distribution showed strikingly similar behavior. The tail of the distribution seemed to decrease as a power-law. This gave rise to a large body of research, studying the impact of power-law distributions on other network properties and designing models for networks that have such power-law degree distributions. It also led to many claims about the universality of power-laws in real-world networks and the underlying causes for this, fueling generations of network scientists. All of this came to an abrupt halt, when a paper in 2019 claimed, based on statistical analysis of a large body of networks, that power-laws are actually very rare. This then led to a heated debate among scientists about the existence of power-laws in networks.'

'In this talk I will address the problem of inferring the existence of power-laws in networks. I will explain that part of the problem is a lack of a proper definition of what these power-laws are. The other is that when researchers do use a definition, this is too restrictive and hence leads to the conclusion that power-laws are rare. We will see how this problem can be addressed using Extreme-Value theory and what tools exists to properly study the existence of power-laws in networks. The conclusion is that power laws are not rare or everywhere. The true answer is somewhere in the middle.'